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Suggestions on investigations of lobed jet mixing
Aerospace Science and Technology 86 (2019) 415–429
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Suggestions on investigations of lobed jet mixing Zhi-qiang Sheng ∗ , Yu Yao, Yi-hua Xu School of Aircraft Engineering, Nanchang Hangkong University, Nanchang, Jiangxi 330063, China
a r t i c l e
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Article history: Received 31 May 2017 Received in revised form 17 September 2017 Accepted 24 January 2019 Available online 29 January 2019 Keywords: Lobed jet mixing Transverse flow Streamwise vortices Normal vortex ring Heat and mass transfer
a b s t r a c t Jet mixings of different constructional lobed mixers comprised of lobed nozzles with and without a mixing duct were investigated numerically. Based on the heat and mass transfer investigation in the streamwise vortices and the “stretch” and “cut” of the normal vortex ring, suggestions on investigations of lobed jet mixing were provided. A more reasonable mechanism for lobed jet mixing was suggested to be revealed when combined fluid dynamics and heat and mass transfer were being investigated. Differences in fluid dynamics and heat and mass transfer with different constructional lobed mixers meant different mechanisms. © 2019 Elsevier Masson SAS. All rights reserved.
1. Introduction The lobed mixer has been investigated for the underlying physics by many researchers. Anderson [1] and Povinelli [2] concluded that the dominant mechanisms within a lobed mixer are associated with the pressure-driven transverse flows being induced by the lobe geometry and with their development in the mixing region. At the lobe exit, the streamwise vortices are formed by the inviscid turning of the primary and secondary streams, and the passage vortices arise because of the primary stream washing around the lobe troughs in the vicinity of the centerbody. In addition, the horseshoe vortices are generated by the interaction of the inner and outer boundary layers with the leading edges of the lobes. Paterson [3] found that, although small-scale vortices shedding at the lobe’s trailing edge cause lateral spreading of the shear layers, which results in enhanced mixing while the lobed geometry increases the length of the interface, it is the large-scale transverse flows that dominate the mixing process by providing rapid transport of heat and axial momentum, contorting the mixing layer interface and causing radial–circumferential mixing of the two streams throughout the axial extent of the nozzle. He also revealed that the lobe penetration angle and depth are the parameters that have the greatest effect on the transverse flow velocity and scale, respectively. Werle et al. [4] observed the process in which the streamwise vortices form, intensify, and then break down. They suggested that
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Corresponding author. E-mail address: [email protected] (Z.-q. Sheng).
https://doi.org/10.1016/j.ast.2019.01.042 1270-9638/© 2019 Elsevier Masson SAS. All rights reserved.
the streamwise vortices formation process is dominantly an inviscid one and found that, in the turbulent case, very intensive microscale mixing occurred within the vortex structure. Skebe et al. [5] further suggested that the flows within lobed mixers are predominantly inviscid, and the streamwise vortices are basically inviscid in origin. In addition, they give an expression to estimate the streamwise circulation. Eckerl et al. [6] also observed the evolvement of the streamwise vortices. They suggested that the large-scale streamwise vortices only result in fluid transport from stream to stream. The vortex breakdown, resulting in a significant increase in turbulent mixing, is required to mix the two flows together homogeneously. Therefore, they proposed that the viscous effects are important in the mixing process downstream of lobed mixers. Ukeiley et al. [7] also found that the flow becomes more homogeneous after the streamwise vortices break down. Elliott et al. [8] found that both the streamwise vortices and the increased initial interfacial area are significant in increasing the mixing, and the amount by which the streamwise vortices augments mixing increases with the velocity ratio of the two streams. They revealed that the normal vortex ring and the streamwise vortices interact to increase the effective entrainment thickness of the mixing layer. McCormick et al. [9] observed that the normal vortex ring is shed from the trailing edge of the lobed mixer, and the streamwise vortices deform the normal vortex ring into a pinchedoff structure that creates intense small-scale turbulence and mixing. Yu et al. [10] suggested that the strength of the streamwise vortices is correlated with the geometrical conditions, and a higher strength of the streamwise vortices would result in a faster rate of achieving spatial uniformity at a fixed downstream distance.
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Definition of abbreviations NLN-25, -35, and -45 Normal lobed nozzles with lobe penetrating angle of 25◦ , 35◦ , and 45◦ , respectively SwALN-25, -35, and -45 Sword alternating-lobe nozzles modified from NLN-25, -35, and -45, respectively Vorx-side walls The streamwise vortices off the side walls
They found that the mixing for the velocity ratio 1 : 1 of the primary stream to the secondary stream is affected not only by the strength of the streamwise vortices, but also by the boundary layer thickness growth. For the higher velocity ratios of 1 : 2 and 1 : 3, a high-turbulence region appears at around two to three lobewavelengths downstream. They suggest that the high-turbulence region responsible for rapid mixing is due to the positive production of turbulent kinetic energy. Belovich et al. [11] also attributed the highly enhanced mixing to the increased strength of the streamwise vortices, and revealed that the presence of the normal vortex ring and their interaction with the streamwise vortices are crucial for enhanced mixing. They found that the fraction of mixing enhancement due to the streamwise vortices (relative to the mixing enhancement due to increased interfacial contact area) is increased as velocity ratio is increased, and this fraction also increased with the downstream distance. Belovich et al. [12] later found that different velocity ratios of the primary stream to the secondary stream result in different mixing mechanisms. For the 3 : 1 case, the streamwise vortices and normal vortex ring interact together to spread the inner jet. The case of 1 : 1 velocity ratio relies mainly on the streamwise vortices to mix the two streams. For mixing with the flow condition 1 : 3, little or no streamwise vorticity were measured. Tsui et al. [13] suggested that the effective mixing process is mainly caused by the streamwise vortices, and the mixing rate is correlated to the streamwise circulation. They found that the contact surface is distorted and elongated to facilitate convective transport by the streamwise vortices, and the turbulent diffusion generated by the streamwise and normal vortices helps increase the interfacial thickness. O’Sullivan et al. [14] found that there is no benefit, in terms of creation of trailing streamwise circulation, in increasing the penetration angle above 30◦ because of increased boundary-layer blockage, and flow separation first occurred at the penetration angle of 35◦ . They also found that, as the lobe penetration angle was increased, the total pressure loss increased and the thrust decreased. For lobe penetration angles less than 30◦ , the variation in the loss with penetration angle is mainly caused by the loss of kinetic energy associated with the swirl imparted to the streams. For larger penetration angles, the losses continued to increase because of retardation and eventual separation of the flow in the lobe troughs. Tew et al. [15] revealed that, with increasing lobe height-to-wavelength ratio, the effectiveness of streamwise vortices decreases, and for the higher height-to-wavelength ratios, a net performance penalty is associated with the addition of streamwise vorticity. Hu et al. [16–18] found that the streamwise vortices can accelerate the “cut” process of the normal vortex ring, and the interaction between the streamwise vortices and normal vortex ring results in creation of much small-scale intense turbulence and enhances the mixing of the jet flow with ambient flow. They observed that, compared with a circular jet flow, the lobed jet flow has a shorter laminar region, smaller scale of spanwise normal vortices, earlier appearance of small-scale turbulent structures, more rapid growth of the shear layer, and quicker decay of the central line velocity. They concluded that the intensive mixing of the core
Vorx-deep troughs The streamwise vortices off the sword deep troughs Vorx-side walls-deep troughs The streamwise vortices off the side walls of the deep troughs Vorx-side walls-shallow troughs The streamwise vortices off the side walls of the shallow troughs
jet flow with ambient flow is concentrated within the first two nozzle diameters in the lobed mixing flow. Hu et al. [19–22] later found that the large-scale streamwise vortices break down into smaller vortices as they travel downstream, which would enhance both large-scale and small-scale mixing. They suggest that, because of the interaction with streamwise vortices, the normal vortex ring deforms into pinched-off structures first, and then, breaks into disconnected substructures as it travels downstream. Nastase et al. [23–27] found that the lobed geometry introduces local transverse shear, which breaks down the normal vortex ring into “ring segments”, streamwise structures that continuously develop and control the entrainment in the near field of the daisy-shaped jet independently of the normal vortex ring passing. Different constructional lobed mixers investigated by the researchers above comprise turbofan-forced mixer nozzles in the investigations of Anderson [1], Povinelli [2], Paterson [3], and Tsui et al. [13], splitter plates with lobed trailing edge in the investigations of Werle et al. [4], Skebe et al. [5], Eckerl et al. [6], Ukeiley et al. [7], Elliott et al. [8], McCormick et al. [9], Yu et al. [10], O’Sullivan et al. [14], and Tew et al. [15], coaxial geometries with a central lobed nozzle adopted by Belovich et al. [11,12], and lobed mixers without a mixing duct adopted by Hu et al. [16–22] and Nastase et al. [23–27]. Further, the lobed jet mixing mechanisms were investigated almost entirely from the fluid dynamics perspective. However, in a previous investigation [28], the largescale mixing rate was concluded to be related to the intensity of the heat and mass transfer (convective heat and mass transfer) attainable in the streamwise vortices. The “stretch” and “cut” of the normal vortex ring are determined by the heat and mass transfer and mixing process. In [29], the sides of the streamwise vortices in which the primary and secondary streams came into contact with each other were suggested to be able to be divided into three segments: windward, sideward, and leeward. Based on this, the heat and mass transfer process in the streamwise vortices was explored preliminarily. Therefore, in the present study, jet mixings of different constructional lobed mixers comprised of lobed nozzles with and without a mixing duct were investigated numerically. By further investigating the heat and mass transfer process in the streamwise vortices and the “stretch” and “cut” of the normal vortex ring, suggestions on investigations of lobed jet mixing were given. 2. Geometrical configurations Fig. 1 shows the model of a lobed nozzle with a mixing duct, where the nozzle is a normal lobed nozzle with a lobe penetration angle of 25◦ (NLN-25). Correspondingly, a lobed nozzle without a mixing duct is the same mixer with the mixing duct removed leaving only the lobed nozzle. The annular entrance of the nozzle is formed by two circles with diameters of 210 and 400 mm. The annular section is smoothly transformed into a circular one through a cone of length of 262.5 mm. The inward and outward lobe penetration angles of NLN-25 are 12.9◦ and 12.1◦ , respectively. The diameters of the circles at the lobe peaks and troughs are, respectively, 550 and 240 mm. The distance from the exit to
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Fig. 1. Geometrical dimensions of NLN-25 with a mixing duct.
Fig. 2. SwALN. Table 1 Several geometry dimensions of lobed nozzles.
SwALN-25 SwALN-35 SwALN-45
α1 /◦
α2 /◦
β /◦
l/mm
12.1 17 21.9
12.9 18 23.2
40 30 24
146.8 146.2 146.5
the entrance is 600 mm, and the exit has an equivalent diameter d of 400 mm. The mixing duct is 1150 mm long, and its entrance is 100 mm ahead of the nozzle exit. The diameter D of the duct is 700 mm, which gives a length-to-diameter ratio of the mixing segment, L / D, of 1.5. As shown in Fig. 2, a sword alternating-lobe nozzle (SwALN25, 35, and 45) is produced by scarfing to remove a part of the lobe troughs and sidewalls of NLN (NLN-25, 35, and 45), and then smoothly extending a sword spoiler (sword deep trough) from all other new troughs. For NLN, the shapes and locations of the exits are the same. In SwALN, the positions of the end tips of the sword spoilers are maintained constant. α1 and α2 are the outward and inward lobe penetration angles of NLN, respectively; β is the scarfing angle; l denotes the radial positions of the shallow troughs. Correspondingly, these dimensions are given in Table 1. 3. Numerical simulation method The simulation domain is shown in Fig. 3(a). Fig. 3(b) shows the surface mesh of SwALN-25. Tetrahedral cells were adopted to discretize the simulation domain. In addition, three-layer prism cells were used as the boundary cells with a first layer height of 0.05 mm. In the simulations conducted in this study, the maximum value of Y + was less than 2.5. As indicated by the arrow in Fig. 3(a), a refinement domain was employed, in which velocity and temperature changed drastically, and the maximum size of the cells in this domain was set to 15 mm. Accordingly, the number of cells in the refinement domain was more than 20 million, and that outside the domain was approximately 2.2 million. The simulation was performed using FLUENT software and SST k–ω turbulence model. SIMPLE algorithm was used to solve the
pressure–velocity coupling. All convection terms were discretized by a second-order scheme. The pressure inlet and pressure outlet conditions were set to far-field, where the operating pressure was 101,325 Pa, temperature was 300 K, and turbulent intensity was 5%. A velocity of 125 m/s, temperature of 850 K, and turbulent intensity of 5% were assigned to the jet inlet. The Reynolds number, based on the equivalent diameter d and the jet conditions, was approximately 2 × 106 . Figs. 4 and 5 compare the numerical simulation results obtained for a six-lobe nozzle with Hu’s experimental results [22]. As Fig. 4 shows, the distribution of the primary and secondary streams obtained by numerical simulation using the SST k–ω turbulence model agrees better with the experimental data than the distribution obtained using the realizable k–ε turbulence model (as show by the difference in the core region). Also investigations [30–34] suggested that the SST k–ω turbulence model can provide accurate prediction of lobed jet mixing flow. As Fig. 5 shows, the simulation results yielded good accuracy for the maximum value of the streamwise vorticity obtained using the SST k–ω turbulence model up to the point at which the vortices broke down but exhibited some discrepancies beyond that point. As most of the enhanced mixing caused by the special geometry of the lobed nozzle is concentrated within the first two diameters of the nozzle [22], the difference in vorticity after breakdown should only have a slight influence on the accuracy of the simulated jet mixing. Figs. 4 and 5 validate the numerical simulation method used in the present study. To determine a suitable mesh density, a SwALN simulation domain was discretized with three different densities. The maximum sizes of the cells used in the refinement domains were 20, 15, and 12 mm, and the number of cells inside and outside of these refinement domains is given in Table 2. Fig. 6 presents 700-K temperature isosurfaces (a quantity with a three-dimensional distribution in the mixing field) simulated with these meshes. As Fig. 6 shows, the number of cells in the simulation domain increases sharply as the maximum size decreases, creating a more refined temperature isosurface. When the maximum size was set to 20 mm, the temperature isosurface was quite rough; conversely, when the
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Fig. 3. Numerical simulation model.
Fig. 4. Experimental and simulated velocity vector and axial velocity distribution of a six-lobe nozzle [35,36]. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)
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Fig. 5. Experimental and simulated maximum decay of streamwise vorticity for a six-lobe nozzle [28,35,36]. Table 2 Number of cells for three different densities used to discretize the simulation domain of a SwALN [35,36]. Maximum size, mm Number inside the refinement domain, millions Number outside the refinement domain, millions
20 12.63 1.61
15 20.81 2.21
12 35.31 2.99
maximum size was set to 12 mm, the number of cells became prohibitively high. When the maximum size was set to 15 mm, the number of cells was still quite reasonable, but the temperature isosurface obtained was similar to that obtained with the maximum size of 12 mm in every region. Therefore, a maximum size of 15 mm was adopted in the refinement domain for all of the subsequent investigations. 4. Results and discussion 4.1. Primary stream distribution and mixing Figs. 7 and 8 show 700 K temperature isosurfaces in mixing fields of lobed nozzles with and without a mixing duct, respectively. As shown in Fig. 7, for lobed nozzles with a mixing duct, such as NLN-25, the primary stream mixing in the region off the side walls is faster near the lobe troughs than near the lobe peaks. The mixing is slowly in the region off the lobe peaks, so that some fraction of the primary stream impinges on the duct before the complete mixing. In the core region, the primary stream has a large section area that decreases slowly and thus needs a long distance for complete mixing. When modified to SwALN-25, the primary stream mixing in the region off the side walls is promoted drastically, and that in the region off the lobe peaks is also benefited. The region inside the circle of the lobe troughs intersects with a small core region and the region between the deep and shallow troughs. The primary stream mixing in the region between the deep and shallow troughs is slightly faster than that in the region off the lobe peaks. In the core region, the primary stream presents a much smaller section area than in the previous case, therefore its complete-mixing distance is clearly decreased. Fig. 8 shows lobed nozzles without a mixing duct for comparison with their ducted versions. For NLN-25, in the region off the lobe peaks, the primary stream mixing is clearly enhanced, and its outwards penetration angle is decreased. In contrast, in the core region, the section area decrease of the primary stream becomes
slower, which means a longer complete-mixing distance. The transformation of the mixing in SwALN-25 is the same as NLN-25 in the region off the lobe peaks, although the primary stream mixing is slightly faster than in NLN-25. However, the primary stream mixing in the region between the deep and shallow troughs is slightly slower. In the core region, the section area decrease of the primary stream also becomes clearly slower. As the lobe penetration angle is increased (Figs. 7 and 8), in the region off the lobe peaks, the outwards penetration angle of the primary stream is increased. Except for more primary stream impinges on the duct in the configuration with a mixing duct, which causes the mixing to slow down, the mixing in regions becomes faster for the same lobed nozzle patterns. 4.2. Transverse flow and streamwise vortices Figs. 9 and 10 show the velocity vector and temperature distributions of lobed nozzles-25 and -45 with and without a mixing duct, respectively. In these figures, the color of the velocity vectors represents the temperature of the local stream, and the scaling factors of the velocity vectors are all kept the same. In addition, 0.25d, 0.50d, and 1.0d are the downstream locations away from the exit of NLN (d = 400 mm). In the configuration with a mixing duct, as shown in Fig. 9, for NLN-25, the streamwise vortices are formed in the region off the side walls (the streamwise vortices off the side walls, Vorx-side walls ) with vortex core placed near the lobe peaks. For SwALN-25, a pair of streamwise vortices is shed from both sides of each sword spoiler (the streamwise vortices off the sword deep troughs, Vorx-deep troughs ). For retarding the inwards radial flow of the secondary stream through the shallow troughs, and the suction of Vorx-deep troughs , the outwards radial flow of the primary stream in the region between the deep and shallow troughs is deflected towards both sides. The streamwise vortices off the side walls of the deep troughs (Vorx-side walls-deep troughs ) have the shape and location that resemble those of the vortex core section of Vorx-side walls in NLN-25, with the radial and circumferential scales smaller than those of Vorx-deep troughs . On the contrary, the streamwise vortices off the side walls of the shallow troughs (Vorx-side walls-shallow troughs ) have the radial location of the vortex core more inwards than that of Vorx-side walls in NLN-25, with the radial and circumferential scales larger than those of Vorx-deep troughs . It can be concluded that the earlier mixing in the modifications when a part of the lobe troughs and side walls is
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Fig. 6. Simulated 700-K temperature isosurfaces of a SwALN with meshes of three different densities [35,36].
Fig. 7. 700 K temperature isosurfaces of lobed nozzles with a mixing duct.
removed and the deflection of the primary stream in the region between the deep and shallow troughs promote the development of Vorx-side walls-shallow troughs , and result in a larger circumferential scale. In the downstream flow of NLN-25, the outwards radial penetration of the primary stream in the region off the lobe peaks has a larger depth than the inwards radial penetration of the secondary stream in the region off the lobe troughs. Vorx-side walls demonstrate that the vortex core moves outwards, the radial and circumferential scales increase, and the vorticity decreases. At 1.0d, Vorx-side walls become very weak, and in the region off the lobe peaks, the outwards radial flow is deflected both sides by the mixing duct, in particular, impingement of the stream on the duct
arises. In the case of SwALN-25, the penetration depth of the primary stream in the region off the lobe peaks is basically equal to that in NLN-25. In addition, the development of Vorx-side walls and impingement of the stream on the duct are similar to those in NLN-25. However, Vorx-deep troughs decrease in the radial scale and increase in the circumferential scale, and the vortex core moves slightly inwards. The two vortex cores at both sides of a sword spoiler separate gradually. At 1.0d, Vorx-deep troughs is weakened, although the swirl is still obvious. As the lobe penetration angle is increased, the transverse flow evolves faster but with a consistent conformation. The weakened Vorx-side walls are strengthened more by the earlier onset of the impingement of the unmixed primary stream on the duct. Moreover,
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Fig. 8. 700 K temperature isosurfaces of lobed nozzles without a mixing duct.
in SwALN, with the unequal scales and radial positions of the two Vorx-side walls of each lobe peak, the distortion of the transverse flow is more severe outside the circle of the shallow troughs. Fig. 9 shows that, in the configuration with a mixing duct, there are two statuses in the heat and mass transfer of the streamwise vortices. The first status is that for Vorx-side walls before the impingement of the stream on the duct, in the windward segment near the lobe troughs, the flow of the secondary stream towards the primary stream is powerful. In the sideward segment, the main flow comprises the mixed stream flowing from the windward segment towards the leeward segment. In the leeward segment near the lobe peaks, the flow is mainly the mixed stream flowing towards the secondary stream, where the primary stream flows mostly radially in the region off the lobe peaks, and the entrainment by the streamwise vortices is weak. Consequently, the windward segment has the fastest mixing, followed by the sideward segment, while the leeward segment has the slowest mixing. For NLN, Vorx-side walls are thin, with a narrow windward segment and a long sideward segment. A small portion of the secondary stream is entrained to flow towards the mixed stream in the sideward segment. For SwALN, although Vorx-side walls-deep troughs are thick, the small scale causes the windward segment to be narrow. On the contrary, Vorx-side walls-shallow troughs have a wider windward segment and a shorter sideward segment because of the large scale and thick shape; therefore, the mixing in the region off the side walls in SwALN is enhanced much more than that in NLN. The second status is that for Vorx-deep troughs , and for Vorx-side walls when the impingement of the stream on the duct occurs, although the heat and mass transfer process is unchanged in the windward and sideward segments, in the leeward segment, not only the mixed stream flows towards the secondary stream,
but also the primary stream is deflected and flows towards the secondary stream. The primary stream will be deflected in the impingement of the stream on the duct, besides that, in the leeward segment of Vorx-deep troughs , the primary stream is deflected to flow towards the secondary stream by the inwards radial flow of the secondary stream. However, it should be noted that the impingement of the stream on the duct decreases the interface area between the primary and secondary streams, which is undesirable for enhancing the mixing. As shown in Fig. 9, in the configuration with a mixing duct, before the impingement of the stream on the duct, the transverse flow of the secondary stream is faint outside the circle of the lobe peaks. However, in the configuration without a mixing duct, as shown in Fig. 10, for the absence of the obstruction of the mixing duct, the pressure-driven secondary stream flows towards the axis on the complete circumference. Outside the circle of the lobe peaks, the inwards radial flow of the secondary stream is relatively strong. This difference from the configuration without a mixing duct causes the outwards penetration depth of the primary stream in the region off the lobe peaks to decrease in the downstream flow. Remarkably, in the configuration without a mixing duct, the inwards radial flow of the secondary stream retards the outwards radial flow of the primary stream outside the circle of the lobe peaks. In this retardation, the primary stream is deflected and mixes with the secondary stream. Therefore, for Vorx-side walls , the heat and mass transfer are provided by the second status. Namely, in the leeward segment, not only does the mixed stream flow towards the secondary stream, but also the primary stream is deflected and flows towards the secondary stream. In Fig. 8, the mixing in the region off the lobe peaks is faster than that in the configuration with a mixing duct. This is mainly caused by the primary stream being
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Fig. 9. Velocity vector and temperature distributions of lobed nozzles-25 and -45 with a mixing duct.
mixed when it is retarded and deflected by the secondary stream. In addition, the mixing efficiency of the windward and sideward segments is not weakened. The reason for the primary stream mixing slower in the core region and the region between the deep and shallow troughs is that the secondary stream available for the mixing is decreased, because of more mixed stream being entrained by the secondary stream and flowing to the windward segment. It also can be seen in Figs. 9 and 10 how the windward, sideward, and leeward segments evolve with the mixing process. Augmenting the lobe penetration angle can increase the radial pene-
tration depth of the primary and secondary streams and promote the heat and mass transfer process of the streamwise vortices, and thus enhance the mixing. The non-dimensional streamwise vorticity ωx and normal vorticity ωn are defined as:
∂w ∂v ωx = − uP ∂ y ∂z 2 2 ∂u D ∂u ∂ w ∂v ωn = − + − uP ∂z ∂x ∂x ∂ y D
(1)
(2)
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Fig. 10. Velocity vector and temperature distributions of lobed nozzles-25 and -45 without a mixing duct.
where D is the diameter of the mixing duct, u P is the initial velocity of the primary stream, and u, v, and w are the velocities in the x, y, and z directions of the mixing stream, respectively. Fig. 11 shows the non-dimensional streamwise vorticity distribution at 0.25d of lobed nozzles-25 and -45 with and without a mixing duct. It demonstrates that the initial streamwise vorticity is greatly enhanced as the lobe penetration angle is increased. On the contrary, while NLN and SwALN with the same lobe penetration angle have similar peak values of the initial Vorx-side walls , the
mixing in the region off the side walls of SwALN is obviously faster, both with and without a mixing duct. Moreover, the peak values of initial Vorx-side walls are smaller when without the mixing duct, but the mixing in the region off the side walls is not inferior to that with the mixing duct. This proves that the mixing rate of the largescale mixing dominated by the streamwise vortices has no certain relationship with the initial streamwise vorticity distribution. The streamwise vorticity only reflects the intensity of the transverse flows that form the vortex. The mixing enhancement by augment-
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Fig. 11. Non-dimensional streamwise vorticity distributions at 0.25d of lobed nozzles-25 and -45 with and without a mixing duct.
ing the lobe penetration angle should actually be attributed to the ability of the accelerated transverse flows of the primary and secondary streams to promote the heat and mass transfer process. 4.3. Axial flow and normal vortices Fig. 12 shows the axial velocity and temperature distributions in contour line and color-coded formats, respectively, for lobed nozzles-25 with and without a mixing duct. As shown in Fig. 12, at 0.25d in the configuration with a mixing duct, the unmixed secondary stream has an axial velocity between 20 and 30 m/s in the passage outside the lobe trough. In the downstream flow, the low speed secondary stream radially moves inwards in the passage outside the lobe trough. On the contrary, at 0.25d in the configuration without a mixing duct, the unmixed secondary stream has an axial velocity lower than 10 m/s in the passage outside the lobe trough. In the downstream flow, the contour line of 10 m/s shifts from the lobe trough to lobe peak, i.e. the axial velocity of the stream increases in the passage outside the lobe trough. Therefore, it is obvious that in the configuration with a mixing duct, the secondary stream is pumped from the entrance of the duct and then flows to downstream region because of the obstruction of the mixing duct. The transverse flow of the secondary stream is created by the geometry of the lobed nozzle only. Thus, in the passage outside the lobe trough, the inwards radial flow of the secondary stream is strong. However, outside the circle of the lobe peaks, the transverse flow of the secondary stream is faint.
In contrast, in the configuration without the mixing duct, the secondary stream flows towards the primary stream from the front and circumference with the entrainment of the primary stream, and flows with it to the downstream region. Here, both the geometry of the lobed nozzle and the entrainment of the primary stream contribute to the transverse flow of the secondary stream. Thus, not only is the transverse flow of the secondary stream strong in the passage outside the lobe trough, but also the inwards radial flow of the secondary stream is relatively strong outside the circle of the lobe peaks. The normal vortex ring is formed for the axial velocity gradient at the interface between the primary and secondary streams in the mixing flow field of a lobed mixer. Therefore, its contortion is related with the shape of the interface, and its vorticity is determined by the axial velocity gradient. Figs. 13 and 14 show the non-dimensional normal vorticity distribution at 0.50d and 1.0d of lobed nozzles-25 and -45 with and without a mixing duct, respectively. Contrasting Figs. 13 and 14 with Fig. 12, after eliminating the influences of the penetration of the primary and secondary streams in the radial direction, and the impingement of the stream on the duct, it can be seen that the effects of the streamwise vortices on the normal vortex ring, essentially, are determined by the heat and mass transfer and mixing process in the windward, sideward, and leeward segments. For the streamwise vortices with the first status in heat and mass transfer, as shown in Figs. 12 and 13, in the regions off the side walls of NLN and the side walls of the shallow troughs
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Fig. 12. Axial velocity (m/s) and temperature distributions of lobed nozzles-25 with and without a mixing duct.
of SwALN in the configuration with a mixing duct, the interface between the primary and secondary streams is stretched towards the side of the primary stream in the windward segment near the lobe trough, with the fastest decrease in the axial velocity gradient. This decrease is shifted from the lobe trough to lobe peak. In the leeward segment near the lobe peak, the interface is stretched towards the side of the secondary stream, with the lowest decrease in the axial velocity gradient, and this stretch is smaller than that near the lobe trough.
For the streamwise vortices with the second status in heat and mass transfer, as shown in Figs. 12 and 14, in the regions off the side walls of NLN and the side walls of the shallow troughs of SwALN in the configuration without a mixing duct, the effects of the streamwise vortices on the normal vortex ring are similar to the first status. The “stretch” and “cut” evolvement of the normal vortex ring is basically unchanged. The difference in the leeward segment, which arose from the difference of heat and mass transfer, demonstrates that the stretch of the interface near the lobe
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Fig. 13. Non-dimensional normal vorticity distribution at 0.50d and 1.0d of lobed nozzles-25 and -45 with a mixing duct.
peak towards the side of the secondary stream is stronger than that in the configuration with a mixing duct; in particular, the “stretch” of normal vortex ring is enhanced in the leeward segment. In the configuration without a mixing duct, outside the circle of the lobe peaks, the inwards radial flow of the secondary stream retards the outwards radial flow of the primary stream and mixes with it. Therefore, in the region off the lobe peaks, the outwards radial move of the interface is smaller, with faster decrease in the axial velocity gradient. Accordingly, the motion of the normal vortex ring is smaller, but the vorticity is decreased quicker. In addition, as more mixed stream is entrained by the secondary stream and flows to the windward segment, in the passage outside the lobe troughs, the contour line of 10 m/s shifts from the lobe trough to lobe peak, and the axial velocity of the stream increases, which promotes the decrement in the axial velocity gradient in the windward segment and consequently the “cut” of the normal vortex ring. In both configurations, Vorx-side walls-shallow troughs in SwALN have a larger circumferential scale than that of Vorx-side walls in NLN. Accordingly, a wider windward segment produces a larger stretch of the interface in the region off the side walls of the shallow troughs, along with a faster decrease in the axial velocity gradient. Therefore, the streamwise vortices with a larger circumferential scale have a wider windward segment, and consequently, demonstrate that in the windward segment, the mixing is faster, and the nor-
mal vortex ring is stretched more with a quicker decrement in the vorticity, which means an earlier “cut” of the ring. Augmenting the lobe penetration angle can promote the “stretch” and “cut” evolvement of the normal vortices ring. 4.4. Discussion With regard to the study of lobed jet mixing, when only the fluid dynamics in the mixing field is studied (such as the evolutions of the streamwise vortices and non-dimensional streamwise vorticity, and the evolutions of the normal vortex ring and nondimensional normal vorticity), the mixing process of the primary stream or even the evolution of the normal vortex ring in all regions cannot be explained accurately. However, referring to the analysis about the jet mixings of lobed nozzles with and without a mixing duct in this paper, when the transverse flows of the primary and secondary streams and the large-scale heat and mass transfer in the transverse flows are studied, the mixing process can be described and the mixed results can be analyzed in detail. It will be known that the large-scale mixing is directly related to the large-scale heat and mass transfer [28]. Therefore, high performance lobed nozzle configurations can be designed by optimizing the distribution of the primary and secondary streams and the large-scale heat and mass transfer [28,29,35,36]. It should be agreed that the lobed jet mixing mostly is the large-scale and small-scale heat and mass transfers, thus the fluid dynamics and
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Fig. 14. Non-dimensional normal vorticity distribution at 0.50d and 1.0d of lobed nozzles-25 and -45 without a mixing duct.
heat and mass transfer should be combined to study the lobed jet mixing mechanisms. In this study, different transverse flows of the primary and secondary streams lead to differences in the large-scale heat and mass transfer for the lobed nozzle with and without a mixing duct at far-field velocity of 0 m/s, which means different mixing mechanisms format different mixing fields. As a result of a follow-up study which the far-field velocity (or initial velocity of the secondary stream) is increased, Fig. 15 shows the 700 K temperature isosurfaces for a coplanar alternating-lobe nozzle (CALN) [28,29] with and without a mixing duct at far-field velocities of 0 and 25 m/s and in a coaxial jet with coaxial jet velocity of 25 m/s and far-field velocity of 0 m/s. It can be seen that when the initial velocity of the secondary stream increases to a certain value (about 25 m/s in this study), the flow of the secondary stream can supply the pump or entrainment of the primary stream, thus the transverse flow of the secondary stream only caused by the lobed nozzle geometry. Finally, the three configurations lobed mixers have almost the same mixing process of the primary stream when the impingement of the primary stream on the duct absents in the mixer with a mixing duct (see Fig. 15(b)).
and mass transfer process in the streamwise vortices and the “stretch” and “cut” of the normal vortex ring, the following suggestions on the investigations of lobed jet mixing were provided:
5. Conclusions
Acknowledgements
In the present study, jet mixings of different constructional lobed mixers comprised of lobed nozzles with and without a mixing duct were investigated numerically. By investigating the heat
The authors gratefully acknowledge the financial support for this project from the National Natural Science Foundation of China under Grants 11862016, 51666012, 51866010.
(1) The lobed jet mixing mechanisms were investigated almost entirely from the fluid dynamics perspective in former investigations. Present investigations indicate that the heat and mass transfer in lobed jet mixing should not be neglected. A more reasonable mechanism for lobed jet mixing was suggested to be revealed when combined fluid dynamics and heat and mass transfer were being investigated. (2) Former investigations of lobed jet mixing adopted different constructional lobed mixers. Accordingly, in present investigation, differences in fluid dynamics and heat and mass transfer with different constructional lobed mixers meant different mechanisms. Conflict of interest statement None declared.
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Fig. 15. 700 K temperature isosurfaces for CALN with and without a mixing duct at far-field velocities of 0 and 25 m/s and in a coaxial jet with coaxial jet velocity of 25 m/s and far-field velocity of 0 m/s.
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[17] H. Hu, T. Kobayashi, T. Saga, et al., Particle image velocimetry and planar laserinduced fluorescence measurements on lobed jet mixing flows, Exp. Fluids 29 (7) (2000) 141–157. [18] H. Hu, T. Saga, T. Kobayashi, et al., Research on the vortical and turbulent structures in the lobed jet flow using laser induced fluorescence and particle image velocimetry techniques, Meas. Sci. Technol. 11 (2000) 698–711. [19] H. Hu, T. Saga, T. Kobayashi, et al., A study on a lobed jet mixing flow by using stereoscopic particle image velocimetry technique, Phys. Fluids 13 (11) (2001) 3425–3441. [20] H. Li, H. Hu, T. Kobayashi, et al., Wavelet multiresolution analysis of stereoscopic particle-image-velocimetry measurements in lobed jet, AIAA J. 40 (6) (2002) 1037–1046. [21] H. Hu, T. Saga, T. Kobayashi, et al., Mixing process in a lobed jet flow, AIAA J. 40 (7) (2002) 1339–1345. [22] H. Hu, T. Saga, T. Kobayashi, et al., Dual-plane stereoscopic PIV measurements in a lobed jet mixing flow, AIAA Paper 2005-0443. [23] A. Meslem, I. Nastase, K. Abed-Meraim, Experimental investigation of the mixing performance of a lobed jet flow, J. Eng. Phys. Thermophys. 81 (1) (2008) 106–111. [24] I. Nastase, A. Meslem, Vortex dynamics and entrainment mechanisms in low Reynolds orifice jets, J. Vis. 11 (4) (2008) 309–318. [25] I. Nastase, A. Meslem, P. Gervais, Primary and secondary vertical structures contribution in the entrainment of low Reynolds number jet flows, Exp. Fluids 44 (6) (2008) 1027–1033. [26] I. Nastase, A. Meslem, Vortex dynamics and mass entrainment in turbulent lobed jets with and without lobe deflection angles, Exp. Fluids 48 (4) (2010) 693–714. [27] A. Meslem, M.E. Hassan, I. Nastase, Analysis of jet entrainment mechanism in the transitional regime by time-resolved PIV, J. Vis. 14 (2011) 41–52. [28] Z.Q. Sheng, S.C. Chen, Z. Wu, et al., High mixing effectiveness lobed nozzles and mixing mechanisms, Sci. China, Technol. Sci. 58 (7) (2015) 1218–1233. [29] Z.Q. Sheng, P.L. Huang, T. Zhao, et al., Configurations of lobed nozzles for high mixing effectiveness, Int. J. Heat Mass Transf. 91 (2015) 671–683. [30] A. Wright, Z.J. Lei, A. Mahallati, et al., Effects of scalloping on the mixing mechanisms of forced mixers with highly swirling core flow, J. Eng. Gas Turbines Power 135 (2013) 071202.
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Contents lists available at ScienceDirect
Aerospace Science and Technology www.elsevier.com/locate/aescte
Suggestions on investigations of lobed jet mixing Zhi-qiang Sheng ∗ , Yu Yao, Yi-hua Xu School of Aircraft Engineering, Nanchang Hangkong University, Nanchang, Jiangxi 330063, China
a r t i c l e
i n f o
Article history: Received 31 May 2017 Received in revised form 17 September 2017 Accepted 24 January 2019 Available online 29 January 2019 Keywords: Lobed jet mixing Transverse flow Streamwise vortices Normal vortex ring Heat and mass transfer
a b s t r a c t Jet mixings of different constructional lobed mixers comprised of lobed nozzles with and without a mixing duct were investigated numerically. Based on the heat and mass transfer investigation in the streamwise vortices and the “stretch” and “cut” of the normal vortex ring, suggestions on investigations of lobed jet mixing were provided. A more reasonable mechanism for lobed jet mixing was suggested to be revealed when combined fluid dynamics and heat and mass transfer were being investigated. Differences in fluid dynamics and heat and mass transfer with different constructional lobed mixers meant different mechanisms. © 2019 Elsevier Masson SAS. All rights reserved.
1. Introduction The lobed mixer has been investigated for the underlying physics by many researchers. Anderson [1] and Povinelli [2] concluded that the dominant mechanisms within a lobed mixer are associated with the pressure-driven transverse flows being induced by the lobe geometry and with their development in the mixing region. At the lobe exit, the streamwise vortices are formed by the inviscid turning of the primary and secondary streams, and the passage vortices arise because of the primary stream washing around the lobe troughs in the vicinity of the centerbody. In addition, the horseshoe vortices are generated by the interaction of the inner and outer boundary layers with the leading edges of the lobes. Paterson [3] found that, although small-scale vortices shedding at the lobe’s trailing edge cause lateral spreading of the shear layers, which results in enhanced mixing while the lobed geometry increases the length of the interface, it is the large-scale transverse flows that dominate the mixing process by providing rapid transport of heat and axial momentum, contorting the mixing layer interface and causing radial–circumferential mixing of the two streams throughout the axial extent of the nozzle. He also revealed that the lobe penetration angle and depth are the parameters that have the greatest effect on the transverse flow velocity and scale, respectively. Werle et al. [4] observed the process in which the streamwise vortices form, intensify, and then break down. They suggested that
*
Corresponding author. E-mail address: [email protected] (Z.-q. Sheng).
https://doi.org/10.1016/j.ast.2019.01.042 1270-9638/© 2019 Elsevier Masson SAS. All rights reserved.
the streamwise vortices formation process is dominantly an inviscid one and found that, in the turbulent case, very intensive microscale mixing occurred within the vortex structure. Skebe et al. [5] further suggested that the flows within lobed mixers are predominantly inviscid, and the streamwise vortices are basically inviscid in origin. In addition, they give an expression to estimate the streamwise circulation. Eckerl et al. [6] also observed the evolvement of the streamwise vortices. They suggested that the large-scale streamwise vortices only result in fluid transport from stream to stream. The vortex breakdown, resulting in a significant increase in turbulent mixing, is required to mix the two flows together homogeneously. Therefore, they proposed that the viscous effects are important in the mixing process downstream of lobed mixers. Ukeiley et al. [7] also found that the flow becomes more homogeneous after the streamwise vortices break down. Elliott et al. [8] found that both the streamwise vortices and the increased initial interfacial area are significant in increasing the mixing, and the amount by which the streamwise vortices augments mixing increases with the velocity ratio of the two streams. They revealed that the normal vortex ring and the streamwise vortices interact to increase the effective entrainment thickness of the mixing layer. McCormick et al. [9] observed that the normal vortex ring is shed from the trailing edge of the lobed mixer, and the streamwise vortices deform the normal vortex ring into a pinchedoff structure that creates intense small-scale turbulence and mixing. Yu et al. [10] suggested that the strength of the streamwise vortices is correlated with the geometrical conditions, and a higher strength of the streamwise vortices would result in a faster rate of achieving spatial uniformity at a fixed downstream distance.
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Definition of abbreviations NLN-25, -35, and -45 Normal lobed nozzles with lobe penetrating angle of 25◦ , 35◦ , and 45◦ , respectively SwALN-25, -35, and -45 Sword alternating-lobe nozzles modified from NLN-25, -35, and -45, respectively Vorx-side walls The streamwise vortices off the side walls
They found that the mixing for the velocity ratio 1 : 1 of the primary stream to the secondary stream is affected not only by the strength of the streamwise vortices, but also by the boundary layer thickness growth. For the higher velocity ratios of 1 : 2 and 1 : 3, a high-turbulence region appears at around two to three lobewavelengths downstream. They suggest that the high-turbulence region responsible for rapid mixing is due to the positive production of turbulent kinetic energy. Belovich et al. [11] also attributed the highly enhanced mixing to the increased strength of the streamwise vortices, and revealed that the presence of the normal vortex ring and their interaction with the streamwise vortices are crucial for enhanced mixing. They found that the fraction of mixing enhancement due to the streamwise vortices (relative to the mixing enhancement due to increased interfacial contact area) is increased as velocity ratio is increased, and this fraction also increased with the downstream distance. Belovich et al. [12] later found that different velocity ratios of the primary stream to the secondary stream result in different mixing mechanisms. For the 3 : 1 case, the streamwise vortices and normal vortex ring interact together to spread the inner jet. The case of 1 : 1 velocity ratio relies mainly on the streamwise vortices to mix the two streams. For mixing with the flow condition 1 : 3, little or no streamwise vorticity were measured. Tsui et al. [13] suggested that the effective mixing process is mainly caused by the streamwise vortices, and the mixing rate is correlated to the streamwise circulation. They found that the contact surface is distorted and elongated to facilitate convective transport by the streamwise vortices, and the turbulent diffusion generated by the streamwise and normal vortices helps increase the interfacial thickness. O’Sullivan et al. [14] found that there is no benefit, in terms of creation of trailing streamwise circulation, in increasing the penetration angle above 30◦ because of increased boundary-layer blockage, and flow separation first occurred at the penetration angle of 35◦ . They also found that, as the lobe penetration angle was increased, the total pressure loss increased and the thrust decreased. For lobe penetration angles less than 30◦ , the variation in the loss with penetration angle is mainly caused by the loss of kinetic energy associated with the swirl imparted to the streams. For larger penetration angles, the losses continued to increase because of retardation and eventual separation of the flow in the lobe troughs. Tew et al. [15] revealed that, with increasing lobe height-to-wavelength ratio, the effectiveness of streamwise vortices decreases, and for the higher height-to-wavelength ratios, a net performance penalty is associated with the addition of streamwise vorticity. Hu et al. [16–18] found that the streamwise vortices can accelerate the “cut” process of the normal vortex ring, and the interaction between the streamwise vortices and normal vortex ring results in creation of much small-scale intense turbulence and enhances the mixing of the jet flow with ambient flow. They observed that, compared with a circular jet flow, the lobed jet flow has a shorter laminar region, smaller scale of spanwise normal vortices, earlier appearance of small-scale turbulent structures, more rapid growth of the shear layer, and quicker decay of the central line velocity. They concluded that the intensive mixing of the core
Vorx-deep troughs The streamwise vortices off the sword deep troughs Vorx-side walls-deep troughs The streamwise vortices off the side walls of the deep troughs Vorx-side walls-shallow troughs The streamwise vortices off the side walls of the shallow troughs
jet flow with ambient flow is concentrated within the first two nozzle diameters in the lobed mixing flow. Hu et al. [19–22] later found that the large-scale streamwise vortices break down into smaller vortices as they travel downstream, which would enhance both large-scale and small-scale mixing. They suggest that, because of the interaction with streamwise vortices, the normal vortex ring deforms into pinched-off structures first, and then, breaks into disconnected substructures as it travels downstream. Nastase et al. [23–27] found that the lobed geometry introduces local transverse shear, which breaks down the normal vortex ring into “ring segments”, streamwise structures that continuously develop and control the entrainment in the near field of the daisy-shaped jet independently of the normal vortex ring passing. Different constructional lobed mixers investigated by the researchers above comprise turbofan-forced mixer nozzles in the investigations of Anderson [1], Povinelli [2], Paterson [3], and Tsui et al. [13], splitter plates with lobed trailing edge in the investigations of Werle et al. [4], Skebe et al. [5], Eckerl et al. [6], Ukeiley et al. [7], Elliott et al. [8], McCormick et al. [9], Yu et al. [10], O’Sullivan et al. [14], and Tew et al. [15], coaxial geometries with a central lobed nozzle adopted by Belovich et al. [11,12], and lobed mixers without a mixing duct adopted by Hu et al. [16–22] and Nastase et al. [23–27]. Further, the lobed jet mixing mechanisms were investigated almost entirely from the fluid dynamics perspective. However, in a previous investigation [28], the largescale mixing rate was concluded to be related to the intensity of the heat and mass transfer (convective heat and mass transfer) attainable in the streamwise vortices. The “stretch” and “cut” of the normal vortex ring are determined by the heat and mass transfer and mixing process. In [29], the sides of the streamwise vortices in which the primary and secondary streams came into contact with each other were suggested to be able to be divided into three segments: windward, sideward, and leeward. Based on this, the heat and mass transfer process in the streamwise vortices was explored preliminarily. Therefore, in the present study, jet mixings of different constructional lobed mixers comprised of lobed nozzles with and without a mixing duct were investigated numerically. By further investigating the heat and mass transfer process in the streamwise vortices and the “stretch” and “cut” of the normal vortex ring, suggestions on investigations of lobed jet mixing were given. 2. Geometrical configurations Fig. 1 shows the model of a lobed nozzle with a mixing duct, where the nozzle is a normal lobed nozzle with a lobe penetration angle of 25◦ (NLN-25). Correspondingly, a lobed nozzle without a mixing duct is the same mixer with the mixing duct removed leaving only the lobed nozzle. The annular entrance of the nozzle is formed by two circles with diameters of 210 and 400 mm. The annular section is smoothly transformed into a circular one through a cone of length of 262.5 mm. The inward and outward lobe penetration angles of NLN-25 are 12.9◦ and 12.1◦ , respectively. The diameters of the circles at the lobe peaks and troughs are, respectively, 550 and 240 mm. The distance from the exit to
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Fig. 1. Geometrical dimensions of NLN-25 with a mixing duct.
Fig. 2. SwALN. Table 1 Several geometry dimensions of lobed nozzles.
SwALN-25 SwALN-35 SwALN-45
α1 /◦
α2 /◦
β /◦
l/mm
12.1 17 21.9
12.9 18 23.2
40 30 24
146.8 146.2 146.5
the entrance is 600 mm, and the exit has an equivalent diameter d of 400 mm. The mixing duct is 1150 mm long, and its entrance is 100 mm ahead of the nozzle exit. The diameter D of the duct is 700 mm, which gives a length-to-diameter ratio of the mixing segment, L / D, of 1.5. As shown in Fig. 2, a sword alternating-lobe nozzle (SwALN25, 35, and 45) is produced by scarfing to remove a part of the lobe troughs and sidewalls of NLN (NLN-25, 35, and 45), and then smoothly extending a sword spoiler (sword deep trough) from all other new troughs. For NLN, the shapes and locations of the exits are the same. In SwALN, the positions of the end tips of the sword spoilers are maintained constant. α1 and α2 are the outward and inward lobe penetration angles of NLN, respectively; β is the scarfing angle; l denotes the radial positions of the shallow troughs. Correspondingly, these dimensions are given in Table 1. 3. Numerical simulation method The simulation domain is shown in Fig. 3(a). Fig. 3(b) shows the surface mesh of SwALN-25. Tetrahedral cells were adopted to discretize the simulation domain. In addition, three-layer prism cells were used as the boundary cells with a first layer height of 0.05 mm. In the simulations conducted in this study, the maximum value of Y + was less than 2.5. As indicated by the arrow in Fig. 3(a), a refinement domain was employed, in which velocity and temperature changed drastically, and the maximum size of the cells in this domain was set to 15 mm. Accordingly, the number of cells in the refinement domain was more than 20 million, and that outside the domain was approximately 2.2 million. The simulation was performed using FLUENT software and SST k–ω turbulence model. SIMPLE algorithm was used to solve the
pressure–velocity coupling. All convection terms were discretized by a second-order scheme. The pressure inlet and pressure outlet conditions were set to far-field, where the operating pressure was 101,325 Pa, temperature was 300 K, and turbulent intensity was 5%. A velocity of 125 m/s, temperature of 850 K, and turbulent intensity of 5% were assigned to the jet inlet. The Reynolds number, based on the equivalent diameter d and the jet conditions, was approximately 2 × 106 . Figs. 4 and 5 compare the numerical simulation results obtained for a six-lobe nozzle with Hu’s experimental results [22]. As Fig. 4 shows, the distribution of the primary and secondary streams obtained by numerical simulation using the SST k–ω turbulence model agrees better with the experimental data than the distribution obtained using the realizable k–ε turbulence model (as show by the difference in the core region). Also investigations [30–34] suggested that the SST k–ω turbulence model can provide accurate prediction of lobed jet mixing flow. As Fig. 5 shows, the simulation results yielded good accuracy for the maximum value of the streamwise vorticity obtained using the SST k–ω turbulence model up to the point at which the vortices broke down but exhibited some discrepancies beyond that point. As most of the enhanced mixing caused by the special geometry of the lobed nozzle is concentrated within the first two diameters of the nozzle [22], the difference in vorticity after breakdown should only have a slight influence on the accuracy of the simulated jet mixing. Figs. 4 and 5 validate the numerical simulation method used in the present study. To determine a suitable mesh density, a SwALN simulation domain was discretized with three different densities. The maximum sizes of the cells used in the refinement domains were 20, 15, and 12 mm, and the number of cells inside and outside of these refinement domains is given in Table 2. Fig. 6 presents 700-K temperature isosurfaces (a quantity with a three-dimensional distribution in the mixing field) simulated with these meshes. As Fig. 6 shows, the number of cells in the simulation domain increases sharply as the maximum size decreases, creating a more refined temperature isosurface. When the maximum size was set to 20 mm, the temperature isosurface was quite rough; conversely, when the
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Fig. 3. Numerical simulation model.
Fig. 4. Experimental and simulated velocity vector and axial velocity distribution of a six-lobe nozzle [35,36]. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)
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Fig. 5. Experimental and simulated maximum decay of streamwise vorticity for a six-lobe nozzle [28,35,36]. Table 2 Number of cells for three different densities used to discretize the simulation domain of a SwALN [35,36]. Maximum size, mm Number inside the refinement domain, millions Number outside the refinement domain, millions
20 12.63 1.61
15 20.81 2.21
12 35.31 2.99
maximum size was set to 12 mm, the number of cells became prohibitively high. When the maximum size was set to 15 mm, the number of cells was still quite reasonable, but the temperature isosurface obtained was similar to that obtained with the maximum size of 12 mm in every region. Therefore, a maximum size of 15 mm was adopted in the refinement domain for all of the subsequent investigations. 4. Results and discussion 4.1. Primary stream distribution and mixing Figs. 7 and 8 show 700 K temperature isosurfaces in mixing fields of lobed nozzles with and without a mixing duct, respectively. As shown in Fig. 7, for lobed nozzles with a mixing duct, such as NLN-25, the primary stream mixing in the region off the side walls is faster near the lobe troughs than near the lobe peaks. The mixing is slowly in the region off the lobe peaks, so that some fraction of the primary stream impinges on the duct before the complete mixing. In the core region, the primary stream has a large section area that decreases slowly and thus needs a long distance for complete mixing. When modified to SwALN-25, the primary stream mixing in the region off the side walls is promoted drastically, and that in the region off the lobe peaks is also benefited. The region inside the circle of the lobe troughs intersects with a small core region and the region between the deep and shallow troughs. The primary stream mixing in the region between the deep and shallow troughs is slightly faster than that in the region off the lobe peaks. In the core region, the primary stream presents a much smaller section area than in the previous case, therefore its complete-mixing distance is clearly decreased. Fig. 8 shows lobed nozzles without a mixing duct for comparison with their ducted versions. For NLN-25, in the region off the lobe peaks, the primary stream mixing is clearly enhanced, and its outwards penetration angle is decreased. In contrast, in the core region, the section area decrease of the primary stream becomes
slower, which means a longer complete-mixing distance. The transformation of the mixing in SwALN-25 is the same as NLN-25 in the region off the lobe peaks, although the primary stream mixing is slightly faster than in NLN-25. However, the primary stream mixing in the region between the deep and shallow troughs is slightly slower. In the core region, the section area decrease of the primary stream also becomes clearly slower. As the lobe penetration angle is increased (Figs. 7 and 8), in the region off the lobe peaks, the outwards penetration angle of the primary stream is increased. Except for more primary stream impinges on the duct in the configuration with a mixing duct, which causes the mixing to slow down, the mixing in regions becomes faster for the same lobed nozzle patterns. 4.2. Transverse flow and streamwise vortices Figs. 9 and 10 show the velocity vector and temperature distributions of lobed nozzles-25 and -45 with and without a mixing duct, respectively. In these figures, the color of the velocity vectors represents the temperature of the local stream, and the scaling factors of the velocity vectors are all kept the same. In addition, 0.25d, 0.50d, and 1.0d are the downstream locations away from the exit of NLN (d = 400 mm). In the configuration with a mixing duct, as shown in Fig. 9, for NLN-25, the streamwise vortices are formed in the region off the side walls (the streamwise vortices off the side walls, Vorx-side walls ) with vortex core placed near the lobe peaks. For SwALN-25, a pair of streamwise vortices is shed from both sides of each sword spoiler (the streamwise vortices off the sword deep troughs, Vorx-deep troughs ). For retarding the inwards radial flow of the secondary stream through the shallow troughs, and the suction of Vorx-deep troughs , the outwards radial flow of the primary stream in the region between the deep and shallow troughs is deflected towards both sides. The streamwise vortices off the side walls of the deep troughs (Vorx-side walls-deep troughs ) have the shape and location that resemble those of the vortex core section of Vorx-side walls in NLN-25, with the radial and circumferential scales smaller than those of Vorx-deep troughs . On the contrary, the streamwise vortices off the side walls of the shallow troughs (Vorx-side walls-shallow troughs ) have the radial location of the vortex core more inwards than that of Vorx-side walls in NLN-25, with the radial and circumferential scales larger than those of Vorx-deep troughs . It can be concluded that the earlier mixing in the modifications when a part of the lobe troughs and side walls is
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Fig. 6. Simulated 700-K temperature isosurfaces of a SwALN with meshes of three different densities [35,36].
Fig. 7. 700 K temperature isosurfaces of lobed nozzles with a mixing duct.
removed and the deflection of the primary stream in the region between the deep and shallow troughs promote the development of Vorx-side walls-shallow troughs , and result in a larger circumferential scale. In the downstream flow of NLN-25, the outwards radial penetration of the primary stream in the region off the lobe peaks has a larger depth than the inwards radial penetration of the secondary stream in the region off the lobe troughs. Vorx-side walls demonstrate that the vortex core moves outwards, the radial and circumferential scales increase, and the vorticity decreases. At 1.0d, Vorx-side walls become very weak, and in the region off the lobe peaks, the outwards radial flow is deflected both sides by the mixing duct, in particular, impingement of the stream on the duct
arises. In the case of SwALN-25, the penetration depth of the primary stream in the region off the lobe peaks is basically equal to that in NLN-25. In addition, the development of Vorx-side walls and impingement of the stream on the duct are similar to those in NLN-25. However, Vorx-deep troughs decrease in the radial scale and increase in the circumferential scale, and the vortex core moves slightly inwards. The two vortex cores at both sides of a sword spoiler separate gradually. At 1.0d, Vorx-deep troughs is weakened, although the swirl is still obvious. As the lobe penetration angle is increased, the transverse flow evolves faster but with a consistent conformation. The weakened Vorx-side walls are strengthened more by the earlier onset of the impingement of the unmixed primary stream on the duct. Moreover,
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Fig. 8. 700 K temperature isosurfaces of lobed nozzles without a mixing duct.
in SwALN, with the unequal scales and radial positions of the two Vorx-side walls of each lobe peak, the distortion of the transverse flow is more severe outside the circle of the shallow troughs. Fig. 9 shows that, in the configuration with a mixing duct, there are two statuses in the heat and mass transfer of the streamwise vortices. The first status is that for Vorx-side walls before the impingement of the stream on the duct, in the windward segment near the lobe troughs, the flow of the secondary stream towards the primary stream is powerful. In the sideward segment, the main flow comprises the mixed stream flowing from the windward segment towards the leeward segment. In the leeward segment near the lobe peaks, the flow is mainly the mixed stream flowing towards the secondary stream, where the primary stream flows mostly radially in the region off the lobe peaks, and the entrainment by the streamwise vortices is weak. Consequently, the windward segment has the fastest mixing, followed by the sideward segment, while the leeward segment has the slowest mixing. For NLN, Vorx-side walls are thin, with a narrow windward segment and a long sideward segment. A small portion of the secondary stream is entrained to flow towards the mixed stream in the sideward segment. For SwALN, although Vorx-side walls-deep troughs are thick, the small scale causes the windward segment to be narrow. On the contrary, Vorx-side walls-shallow troughs have a wider windward segment and a shorter sideward segment because of the large scale and thick shape; therefore, the mixing in the region off the side walls in SwALN is enhanced much more than that in NLN. The second status is that for Vorx-deep troughs , and for Vorx-side walls when the impingement of the stream on the duct occurs, although the heat and mass transfer process is unchanged in the windward and sideward segments, in the leeward segment, not only the mixed stream flows towards the secondary stream,
but also the primary stream is deflected and flows towards the secondary stream. The primary stream will be deflected in the impingement of the stream on the duct, besides that, in the leeward segment of Vorx-deep troughs , the primary stream is deflected to flow towards the secondary stream by the inwards radial flow of the secondary stream. However, it should be noted that the impingement of the stream on the duct decreases the interface area between the primary and secondary streams, which is undesirable for enhancing the mixing. As shown in Fig. 9, in the configuration with a mixing duct, before the impingement of the stream on the duct, the transverse flow of the secondary stream is faint outside the circle of the lobe peaks. However, in the configuration without a mixing duct, as shown in Fig. 10, for the absence of the obstruction of the mixing duct, the pressure-driven secondary stream flows towards the axis on the complete circumference. Outside the circle of the lobe peaks, the inwards radial flow of the secondary stream is relatively strong. This difference from the configuration without a mixing duct causes the outwards penetration depth of the primary stream in the region off the lobe peaks to decrease in the downstream flow. Remarkably, in the configuration without a mixing duct, the inwards radial flow of the secondary stream retards the outwards radial flow of the primary stream outside the circle of the lobe peaks. In this retardation, the primary stream is deflected and mixes with the secondary stream. Therefore, for Vorx-side walls , the heat and mass transfer are provided by the second status. Namely, in the leeward segment, not only does the mixed stream flow towards the secondary stream, but also the primary stream is deflected and flows towards the secondary stream. In Fig. 8, the mixing in the region off the lobe peaks is faster than that in the configuration with a mixing duct. This is mainly caused by the primary stream being
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Fig. 9. Velocity vector and temperature distributions of lobed nozzles-25 and -45 with a mixing duct.
mixed when it is retarded and deflected by the secondary stream. In addition, the mixing efficiency of the windward and sideward segments is not weakened. The reason for the primary stream mixing slower in the core region and the region between the deep and shallow troughs is that the secondary stream available for the mixing is decreased, because of more mixed stream being entrained by the secondary stream and flowing to the windward segment. It also can be seen in Figs. 9 and 10 how the windward, sideward, and leeward segments evolve with the mixing process. Augmenting the lobe penetration angle can increase the radial pene-
tration depth of the primary and secondary streams and promote the heat and mass transfer process of the streamwise vortices, and thus enhance the mixing. The non-dimensional streamwise vorticity ωx and normal vorticity ωn are defined as:
∂w ∂v ωx = − uP ∂ y ∂z 2 2 ∂u D ∂u ∂ w ∂v ωn = − + − uP ∂z ∂x ∂x ∂ y D
(1)
(2)
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Fig. 10. Velocity vector and temperature distributions of lobed nozzles-25 and -45 without a mixing duct.
where D is the diameter of the mixing duct, u P is the initial velocity of the primary stream, and u, v, and w are the velocities in the x, y, and z directions of the mixing stream, respectively. Fig. 11 shows the non-dimensional streamwise vorticity distribution at 0.25d of lobed nozzles-25 and -45 with and without a mixing duct. It demonstrates that the initial streamwise vorticity is greatly enhanced as the lobe penetration angle is increased. On the contrary, while NLN and SwALN with the same lobe penetration angle have similar peak values of the initial Vorx-side walls , the
mixing in the region off the side walls of SwALN is obviously faster, both with and without a mixing duct. Moreover, the peak values of initial Vorx-side walls are smaller when without the mixing duct, but the mixing in the region off the side walls is not inferior to that with the mixing duct. This proves that the mixing rate of the largescale mixing dominated by the streamwise vortices has no certain relationship with the initial streamwise vorticity distribution. The streamwise vorticity only reflects the intensity of the transverse flows that form the vortex. The mixing enhancement by augment-
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Fig. 11. Non-dimensional streamwise vorticity distributions at 0.25d of lobed nozzles-25 and -45 with and without a mixing duct.
ing the lobe penetration angle should actually be attributed to the ability of the accelerated transverse flows of the primary and secondary streams to promote the heat and mass transfer process. 4.3. Axial flow and normal vortices Fig. 12 shows the axial velocity and temperature distributions in contour line and color-coded formats, respectively, for lobed nozzles-25 with and without a mixing duct. As shown in Fig. 12, at 0.25d in the configuration with a mixing duct, the unmixed secondary stream has an axial velocity between 20 and 30 m/s in the passage outside the lobe trough. In the downstream flow, the low speed secondary stream radially moves inwards in the passage outside the lobe trough. On the contrary, at 0.25d in the configuration without a mixing duct, the unmixed secondary stream has an axial velocity lower than 10 m/s in the passage outside the lobe trough. In the downstream flow, the contour line of 10 m/s shifts from the lobe trough to lobe peak, i.e. the axial velocity of the stream increases in the passage outside the lobe trough. Therefore, it is obvious that in the configuration with a mixing duct, the secondary stream is pumped from the entrance of the duct and then flows to downstream region because of the obstruction of the mixing duct. The transverse flow of the secondary stream is created by the geometry of the lobed nozzle only. Thus, in the passage outside the lobe trough, the inwards radial flow of the secondary stream is strong. However, outside the circle of the lobe peaks, the transverse flow of the secondary stream is faint.
In contrast, in the configuration without the mixing duct, the secondary stream flows towards the primary stream from the front and circumference with the entrainment of the primary stream, and flows with it to the downstream region. Here, both the geometry of the lobed nozzle and the entrainment of the primary stream contribute to the transverse flow of the secondary stream. Thus, not only is the transverse flow of the secondary stream strong in the passage outside the lobe trough, but also the inwards radial flow of the secondary stream is relatively strong outside the circle of the lobe peaks. The normal vortex ring is formed for the axial velocity gradient at the interface between the primary and secondary streams in the mixing flow field of a lobed mixer. Therefore, its contortion is related with the shape of the interface, and its vorticity is determined by the axial velocity gradient. Figs. 13 and 14 show the non-dimensional normal vorticity distribution at 0.50d and 1.0d of lobed nozzles-25 and -45 with and without a mixing duct, respectively. Contrasting Figs. 13 and 14 with Fig. 12, after eliminating the influences of the penetration of the primary and secondary streams in the radial direction, and the impingement of the stream on the duct, it can be seen that the effects of the streamwise vortices on the normal vortex ring, essentially, are determined by the heat and mass transfer and mixing process in the windward, sideward, and leeward segments. For the streamwise vortices with the first status in heat and mass transfer, as shown in Figs. 12 and 13, in the regions off the side walls of NLN and the side walls of the shallow troughs
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Fig. 12. Axial velocity (m/s) and temperature distributions of lobed nozzles-25 with and without a mixing duct.
of SwALN in the configuration with a mixing duct, the interface between the primary and secondary streams is stretched towards the side of the primary stream in the windward segment near the lobe trough, with the fastest decrease in the axial velocity gradient. This decrease is shifted from the lobe trough to lobe peak. In the leeward segment near the lobe peak, the interface is stretched towards the side of the secondary stream, with the lowest decrease in the axial velocity gradient, and this stretch is smaller than that near the lobe trough.
For the streamwise vortices with the second status in heat and mass transfer, as shown in Figs. 12 and 14, in the regions off the side walls of NLN and the side walls of the shallow troughs of SwALN in the configuration without a mixing duct, the effects of the streamwise vortices on the normal vortex ring are similar to the first status. The “stretch” and “cut” evolvement of the normal vortex ring is basically unchanged. The difference in the leeward segment, which arose from the difference of heat and mass transfer, demonstrates that the stretch of the interface near the lobe
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Fig. 13. Non-dimensional normal vorticity distribution at 0.50d and 1.0d of lobed nozzles-25 and -45 with a mixing duct.
peak towards the side of the secondary stream is stronger than that in the configuration with a mixing duct; in particular, the “stretch” of normal vortex ring is enhanced in the leeward segment. In the configuration without a mixing duct, outside the circle of the lobe peaks, the inwards radial flow of the secondary stream retards the outwards radial flow of the primary stream and mixes with it. Therefore, in the region off the lobe peaks, the outwards radial move of the interface is smaller, with faster decrease in the axial velocity gradient. Accordingly, the motion of the normal vortex ring is smaller, but the vorticity is decreased quicker. In addition, as more mixed stream is entrained by the secondary stream and flows to the windward segment, in the passage outside the lobe troughs, the contour line of 10 m/s shifts from the lobe trough to lobe peak, and the axial velocity of the stream increases, which promotes the decrement in the axial velocity gradient in the windward segment and consequently the “cut” of the normal vortex ring. In both configurations, Vorx-side walls-shallow troughs in SwALN have a larger circumferential scale than that of Vorx-side walls in NLN. Accordingly, a wider windward segment produces a larger stretch of the interface in the region off the side walls of the shallow troughs, along with a faster decrease in the axial velocity gradient. Therefore, the streamwise vortices with a larger circumferential scale have a wider windward segment, and consequently, demonstrate that in the windward segment, the mixing is faster, and the nor-
mal vortex ring is stretched more with a quicker decrement in the vorticity, which means an earlier “cut” of the ring. Augmenting the lobe penetration angle can promote the “stretch” and “cut” evolvement of the normal vortices ring. 4.4. Discussion With regard to the study of lobed jet mixing, when only the fluid dynamics in the mixing field is studied (such as the evolutions of the streamwise vortices and non-dimensional streamwise vorticity, and the evolutions of the normal vortex ring and nondimensional normal vorticity), the mixing process of the primary stream or even the evolution of the normal vortex ring in all regions cannot be explained accurately. However, referring to the analysis about the jet mixings of lobed nozzles with and without a mixing duct in this paper, when the transverse flows of the primary and secondary streams and the large-scale heat and mass transfer in the transverse flows are studied, the mixing process can be described and the mixed results can be analyzed in detail. It will be known that the large-scale mixing is directly related to the large-scale heat and mass transfer [28]. Therefore, high performance lobed nozzle configurations can be designed by optimizing the distribution of the primary and secondary streams and the large-scale heat and mass transfer [28,29,35,36]. It should be agreed that the lobed jet mixing mostly is the large-scale and small-scale heat and mass transfers, thus the fluid dynamics and
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Fig. 14. Non-dimensional normal vorticity distribution at 0.50d and 1.0d of lobed nozzles-25 and -45 without a mixing duct.
heat and mass transfer should be combined to study the lobed jet mixing mechanisms. In this study, different transverse flows of the primary and secondary streams lead to differences in the large-scale heat and mass transfer for the lobed nozzle with and without a mixing duct at far-field velocity of 0 m/s, which means different mixing mechanisms format different mixing fields. As a result of a follow-up study which the far-field velocity (or initial velocity of the secondary stream) is increased, Fig. 15 shows the 700 K temperature isosurfaces for a coplanar alternating-lobe nozzle (CALN) [28,29] with and without a mixing duct at far-field velocities of 0 and 25 m/s and in a coaxial jet with coaxial jet velocity of 25 m/s and far-field velocity of 0 m/s. It can be seen that when the initial velocity of the secondary stream increases to a certain value (about 25 m/s in this study), the flow of the secondary stream can supply the pump or entrainment of the primary stream, thus the transverse flow of the secondary stream only caused by the lobed nozzle geometry. Finally, the three configurations lobed mixers have almost the same mixing process of the primary stream when the impingement of the primary stream on the duct absents in the mixer with a mixing duct (see Fig. 15(b)).
and mass transfer process in the streamwise vortices and the “stretch” and “cut” of the normal vortex ring, the following suggestions on the investigations of lobed jet mixing were provided:
5. Conclusions
Acknowledgements
In the present study, jet mixings of different constructional lobed mixers comprised of lobed nozzles with and without a mixing duct were investigated numerically. By investigating the heat
The authors gratefully acknowledge the financial support for this project from the National Natural Science Foundation of China under Grants 11862016, 51666012, 51866010.
(1) The lobed jet mixing mechanisms were investigated almost entirely from the fluid dynamics perspective in former investigations. Present investigations indicate that the heat and mass transfer in lobed jet mixing should not be neglected. A more reasonable mechanism for lobed jet mixing was suggested to be revealed when combined fluid dynamics and heat and mass transfer were being investigated. (2) Former investigations of lobed jet mixing adopted different constructional lobed mixers. Accordingly, in present investigation, differences in fluid dynamics and heat and mass transfer with different constructional lobed mixers meant different mechanisms. Conflict of interest statement None declared.
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Fig. 15. 700 K temperature isosurfaces for CALN with and without a mixing duct at far-field velocities of 0 and 25 m/s and in a coaxial jet with coaxial jet velocity of 25 m/s and far-field velocity of 0 m/s.
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